Hoff, thus rendering perfectly safe his communications in his rear.
(Fig. 7.)

We have said that the configuration of the ground and the position of
the hostile forces may _sometimes_ render it advisable to direct our
line of operations against the extremity of the enemy's line of defence;
but, _as a general rule_ a central direction will lead to more important
results. This severs the enemy's means of resistance, and enables the
assailant to strike, with the mass of his force, upon the dissevered and
partially paralyzed members of the hostile body. (Fig. 8.)

Such a plan of operations enabled Napoleon, in the Italian campaigns of
1796 and 1797, to pierce and destroy, with a small force, the large and
successive armies which Austria sent against him. In 1805 his operations
were both interior and central: in 1808 they were most eminently
central: in 1809, by the central operations in the vicinity of
Ratisbonne, he defeated the large and almost victorious army of the
Archduke Charles: in 1814, from his central position between the Marne
and Seine, with only seventy thousand men against a force of more than
two hundred thousand, he gained numerous victories, and barely failed of
complete success. Again in 1815, with an army of only one hundred and
twenty thousand men against an allied force of two hundred and twenty
thousand, by his central advance on Charleroi and Ligny, he gained a
most decided advantage over the enemy--an advantage lost by the
eccentric movement of Grouchy: and even in 1813, his central position at
Dresden would have secured him most decisive advantages, had not the
faults of his lieutenants lost these advantages in the disasters of Kulm
and the Katzbach.

For the same frontier it is objectionable to form more than one army;